Advertisements
Advertisements
प्रश्न
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
पर्याय
25
`1/25`
5
1
Advertisements
उत्तर
`1/25`
Explanation;
Hint:
5x = sec θ
x = `(sec theta/5)`
∴ x2 = `(sec^2 theta)/25`
`5/x` = tan θ
`1/x = tan theta/5`
`1/x^2 = (tan^2 theta)/25`
`x^2 - 1/x^2 = (sec^2 theta)/25 - (tan^2 theta)/25`
= `(sec^2 theta - tan^2 theta)/25`
= `1/25`
APPEARS IN
संबंधित प्रश्न
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
